**Conjecture**Let be an abelian group. Is the core of a Cayley graph (on some power of ) a Cayley graph (on some power of )?

Even the case is open. In this case, Cayley graphs on some power of are called *cube-like graphs*, they have been introduced by Lov\'asz as an example of graphs, for which every eigenvalue is an integer.

So, in this case we ask, whether a core of each cube-like graph is a cube-like graph.